74.13.14 problem 31

Internal problem ID [16301]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number : 31
Date solved : Thursday, March 13, 2025 at 08:10:10 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+7 y^{\prime \prime \prime }+6 y^{\prime \prime }-32 y^{\prime }-32 y&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 26

ode:=diff(diff(diff(diff(y(t),t),t),t),t)+7*diff(diff(diff(y(t),t),t),t)+6*diff(diff(y(t),t),t)-32*diff(y(t),t)-32*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_{2} {\mathrm e}^{6 t}+c_{1} {\mathrm e}^{3 t}+t c_4 +c_{3} \right ) {\mathrm e}^{-4 t} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 34

ode=D[y[t],{t,4}]+7*D[ y[t],{t,3}]+6*D[y[t],{t,2}]-32*D[y[t],t]-32*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-4 t} \left (c_2 t+c_3 e^{3 t}+c_4 e^{6 t}+c_1\right ) \]

✓ Sympy. Time used: 0.215 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-32*y(t) - 32*Derivative(y(t), t) + 6*Derivative(y(t), (t, 2)) + 7*Derivative(y(t), (t, 3)) + Derivative(y(t), (t, 4)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{3} e^{- t} + C_{4} e^{2 t} + \left (C_{1} + C_{2} t\right ) e^{- 4 t} \]